You can think of the ice cream in a well packed ice cream cone as a half of a sphere added to a cone. If the cone is 4.5 inches tall and 3 inches across, how much ice cream is in the cone? (Round your answer to the nearest 0.1 units.)

Relevance

Volume of a cone: (1/3)*base*height

First, find the volume in the cone. (1/3)*(2.25pi)*(4.5) = 10.6028752

***Base is pi*(radius^2), which is 2.25pi

Then, find the volume of the half sphere. (1/2)*(4/3)*pi*(3.375) = 7.06858347

Add the two parts together, and you get 10.6028752+7.06858347 = 17.6714587

Round this to the nearest 0.1, and you get 17.7 inches cubed.

I hope this is right!

• Since the problem asks how much ice cream is in the cone. This would be the volume of the cone + the volume of the hemisphere that sits on top of the cone.

Formula for Volume of a cone:

V = 1/3(pi)( r^2)( h)

Formula for the volume of a hemisphere:

V=2/3(pi)(r^3)

Add these two formulas together to get

V=1/3(pi)(r^2)(h) + 2/3 (pi)(r^3)

Substitute in vales and solve.

V=1/3(3.14)(1.5^2)(4.5)+2/3(3.14)(1.5^3)

V=17.7 in^3

• First you need the formulas for the volumes:

Cone: pi*r^2*h/3

1/2 Sphere: 1/2*(4/3*pi*r^3) = 2/3*pi*r^3

For this problem, plug in the numbers and add them together:

pi*(3/2)^2*4.5/3 (3/2 b/c radius is half the across distance) + 2/3*pi*(3/2)^3

(in in^3)

Source(s): volume equations from Calculus 8th ed. by Larson, Hostetler, Edwards
• V = 1/3 pi*r^2*h + 1/2 *4/3 * pi * r^3

=> V = 1/3 * 22/7 * 1.5^2 * 4.5 + 1/2 * 4/3 * 22/7 * 1.5^3

= 10.6071 + 7.07143

= 17.7 inch^3

And who is the one that does not agree with me?